An object with a mass of #5 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= xe^x-x #. How much work would it take to move the object over #x in [1, 4], where x is in meters?

1 Answer
Feb 12, 2016

Answer:

#W=147,15(3e^x-7)J#

Explanation:

#W=F_f*x=N int_1^4(x e^x-x) x*d x#
#W=m g int_1^4 (x^2 e^x-x^2)d x#
#W=m g ([e^x(x^2-2 x+2)]_1^4 - [1/3 x^3]_1^4)#
#W=m g(9e^x-21)#
#W=5*9,81(9e^x-21#
#W=147,15(3e^x-7)J#